More like a "lifetime achievement" though, rather than the Nobel Prize, which tends to be for more specific achievements.
All indefinite orthogonal groups of matrices of equal metric signature are isomorphic by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Following the definition of the indefinite orthogonal group, we want to show that only the metric signature matters.
First we can observe that the exact matrices are different. For example, taking the standard matrix of :and:both have the same metric signature. However, we notice that a rotation of 90 degrees, which preserves the first form, does not preserve the second one! E.g. consider the vector , then . But after a rotation of 90 degrees, it becomes , and now ! Therefore, we have to search for an isomorphism between the two sets of matrices.
For example, consider the orthogonal group, which can be defined as shown at the orthogonal group is the group of all matrices that preserve the dot product can be defined as:
Some examples by Ciro Santilli follow.
Of the tutorial-subjectivity type:
- This edit perfectly summarizes how Ciro feels about Wikipedia (no particular hate towards that user, he was a teacher at the prestigious Pierre and Marie Curie University and actually as a wiki page about him):which removed the only diagram that was actually understandable to non-Mathematicians, which Ciro Santilli had created, and received many upvotes at: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426. The removal does not generate any notifications to you unless you follow the page which would lead to infinite noise, and is extremely difficult to find out how to contact the other person. The removal justification is even somewhat ad hominem: how does he know Ciro Santilli is also not a professional Mathematician? :-) Maybe it is obvious because Ciro explains in a way that is understandable. Also removal makes no effort to contact original author. Of course, this is caused by the fact that there must also have been a bunch of useless edits not done by Ciro, and there is no reputation system to see if you should ignore a person or not immediately, so removal author has no patience anymore. This is what makes it impossible to contribute to Wikipedia: your stuff gets deleted at any time, and you don't know how to appeal it. Ciro is going to regret having written this rant after Daniel replies and shows the diagram is crap. But that would be better than not getting a reply and not learning that the diagram is crap.
rm a cryptic diagram (not understandable by a professional mathematician, without further explanations
- en.wikipedia.org/w/index.php?title=Finite_field&type=revision&diff=1044934168&oldid=1044905041 on finite fields with edit comment "Obviously: X ≡ α". Discussion at en.wikipedia.org/wiki/Talk:Finite_field#Concrete_simple_worked_out_example Some people simply don't know how to explain things to beginners, or don't think Wikipedia is where it should be done. One simply can't waste time fighting off those people, writing good tutorials is hard enough in itself without that fight.
- en.wikipedia.org/w/index.php?title=Discrete_Fourier_transform&diff=1193622235&oldid=1193529573 by user Bob K. removed Ciro Santilli's awesome simple image of the Discrete Fourier transform as seen at en.wikipedia.org/w/index.php?title=Discrete_Fourier_transform&oldid=1176616763:with message:
Hello. I am a retired electrical engineer, living near Washington,DC. Most of my contributions are in the area of DSP, where I have about 40 years of experience in applications on many different processors and architectures.
Thank you so much!!remove non-helpful image
Maybe it is a common thread that these old "experts" keep removing anything that is actually intelligible by beginners? Section "There is value in tutorials written by beginners"Also ranted at: x.com/cirosantilli/status/1808862417566290252
Figure 1. Source at: numpy/fft_plot.py. - when Ciro Santilli created Scott Hassan's page, he originally included mentions of his saucy divorce: en.wikipedia.org/w/index.php?title=Scott_Hassan&oldid=1091706391 These were reverted by Scott's puppets three times, and Ciro and two other editors fought back. Finally, Ciro understood that Hassan's puppets were likely right about the removal because you can't talk about private matters of someone who is low profile:even if it is published in well known and reliable publications like the bloody New York Times. In this case, it is clear that most people wanted to see this information summarized on Wikipedia since others fought back Hassan's puppet. This is therefore a failure of Wikipedia to show what the people actually want to read about.This case is similar to the PsiQuantum one. Something is extremely well known in an important niche, and many people want to read about it. But because the average person does not know about this important subject, and you are limited about what you can write about it or not, thus hurting the people who want to know about it.
Notability constraints, which are are way too strict:There are even a Wikis that were created to remove notability constraints: Wiki without notability requirements.
- even information about important companies can be disputed. E.g. once Ciro Santilli tried to create a page for PsiQuantum, a startup with $650m in funding, and there was a deletion proposal because it did not contain verifiable sources not linked directly to information provided by the company itself: en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/PsiQuantum Although this argument is correct, it is also true about 90% of everything that is on Wikipedia about any company. Where else can you get any information about a B2B company? Their clients are not going to say anything. Lawsuits and scandals are kind of the only possible source... In that case, the page was deleted with 2 votes against vs 3 votes for deletion.is very similar to Stack Exchange's own Stack Overflow content deletion issues. Ain't Nobody Got Time For That. "Ain't Nobody Got Time for That" actually has a Wiki page: en.wikipedia.org/wiki/Ain%27t_Nobody_Got_Time_for_That. That's notable. Unlike a $600M+ company of course.
should we delete this extremely likely useful/correct content or not according to this extremely complex system of guidelines"
In December 2023 the page was re-created, and seemed to stick: en.wikipedia.org/wiki/Talk:PsiQuantum#Secondary_sources It's just a random going back and forth. Author Ctjk has an interesting background:I am a legal official at a major government antitrust agency. The only plausible connection is we regulate tech firms
For these reasons reason why Ciro basically only contributes images to Wikipedia: because they are either all in or all out, and you can determine which one of them it is. And this allows images to be more attributable, so people can actually see that it was Ciro that created a given amazing image, thus overcoming Wikipedia's lack of reputation system a little bit as well.
Wikipedia is perfect for things like biographies, geography, or history, which have a much more defined and subjective expository order. But when it comes to "tutorials of how to actually do stuff", which is what mathematics and physics are basically about, Wikipedia has a very hard time to go beyond dry definitions which are only useful for people who already half know the stuff. But to learn from zero, newbies need tutorials with intuition and examples.
Bibliography:
- gwern.net/inclusionism from gwern.net:
Iron Law of Bureaucracy: the downwards deletionism spiral discourages contribution and is how Wikipedia will die.
- Quote "Golden wiki vs Deletionism on Wikipedia"
Per-table dumps created with mysqldump and listed at: dumps.wikimedia.org/. Most notably, for the English Wikipedia: dumps.wikimedia.org/enwiki/latest/
A few of the files are not actual tables but derived data, notably dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz from Download titles of all Wikipedia articles
The tables are "documented" under: www.mediawiki.org/wiki/Manual:Database_layout, e.g. the central "page" table: www.mediawiki.org/wiki/Manual:Page_table. But in many cases it is impossible to deduce what fields are from those docs.
dumps.wikimedia.org/enwiki/latest/enwiki-latest-category.sql.gz contains a list of categories. It only contains the categories and some counts, but it doesn't contain the subcategories and pages under each category, so it is a bit pointless.
The schema is listed at: www.mediawiki.org/wiki/Manual:Category_table
The SQL first defines the table:followed by a few humongous inserts:which we can see at: en.wikipedia.org/wiki/Category:Computer_storage_devices
CREATE TABLE `category` (
`cat_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`cat_title` varbinary(255) NOT NULL DEFAULT '',
`cat_pages` int(11) NOT NULL DEFAULT 0,
`cat_subcats` int(11) NOT NULL DEFAULT 0,
`cat_files` int(11) NOT NULL DEFAULT 0,
PRIMARY KEY (`cat_id`),
UNIQUE KEY `cat_title` (`cat_title`),
KEY `cat_pages` (`cat_pages`)
) ENGINE=InnoDB AUTO_INCREMENT=249228235 DEFAULT CHARSET=binary ROW_FORMAT=COMPRESSED;INSERT INTO `category` VALUES (2,'Unprintworthy_redirects',1597224,20,0),(3,'Computer_storage_devices',88,11,0)Se see that en.wikipedia.org/wiki/Category:Computer_storage_devices_by_companyso it contains only categories.
- en.wikipedia.org/wiki/Category:Computer_storage_devices is a subcategory of that category and it appears in that file.
- en.wikipedia.org/wiki/Acronis_Secure_Zone is a page of the category, and it does not appear
We can check this with:and it shows:There doesn't seem to be any interlink between the categories, only page and subcategory counts therefore.
sed -s 's/),/\n/g' enwiki-latest-category.sql | grep Computer_storage_devices(3,'Computer_storage_devices',88,11,0
(521773,'Computer_storage_devices_by_company',6,6,0dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz Characterization:
- contains redirects, e.g. en.wikipedia.org/wiki/"Ampere_North" redirects to en.wikipedia.org/wiki/Ampere_North,_New_Jersey and both are present. Noted in this comment: stackoverflow.com/questions/24474288/how-to-obtain-a-list-of-titles-of-all-wikipedia-articles#comment136016773_24474476
How to use a single source multiple times in a Wikipedia article? by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16en.wikipedia.org/wiki/Help:Footnotes#Footnotes:_using_a_source_more_than_once gives the following method:
Definition, anywhere on article, likely ideally as the first usage:
<ref name="myname">{{cite web ...}}</ref>And then you can use it later on as:which automatically expands the exact same thing, or using the shortcut:
<ref name="myname" />{{r|myname}}To cite multiple pages of a book: en.wikipedia.org/wiki/Wikipedia:Citing_sources#Citing_multiple_pages_of_the_same_source, the best method is to define and use the reference without adding the Do not set the page in or for multiple pages:
p or location in cite as:<ref name="googleStory">{{cite book |title=The Google Story}}</ref>{{rp|p=123}}cite, otherwise it shows up on the references. Instead we use the {{rp}} template. And then use the reference with the {{r}} template as:{{r|googleStory|p=456}}{{r|googleStory|pp=123, 156-158}}To avoid duplication when citing multiple pages: Section "How to use a single source multiple times in a Wikipedia article?"
A good big sample definition:There is also
<ref name="googleStory">{{cite book |last1=Vise |first1=David |author-link1=David A. Vise |last2=Malseed |first2=Mark |author-link2=Mark Malseed |title=The Google Story |date=2008 |publisher=Delacorte Press |url=https://archive.org/details/isbn_9780385342728}}</ref>title-link to link to a wiki page. But it is incompatible with url= for Internet Archive Open Library links which is a shame. Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact